TY - JOUR
ID - 357
TI - Various topological forms of Von Neumann regularity in Banach algebras
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Esslamzadeh, G.
AU - Shadab, M.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 3
SP - 159
EP - 170
KW - Topologically von Neumann regular
KW - principally von Neumann regular
DO -
N2 - We study topological von Neumann regularity
and principal von Neumann regularity of Banach algebras. Our
main objective is comparing these two types of Banach algebras and
some other known Banach algebras with one another. In particular,
we show that the class of topologically von Neumann regular Banach
algebras contains all $C^*$-algebras, group algebras of compact
abelian groups and certain weakly amenable Banach algebras while
it excludes measure algebras, of certain locally compact Abelian
groups. Moreover, we show that in a unital amenable Banach
algebra, principal regularity implies topological regularity.
Finally, we use topological regularity to obtain some information
about hereditary $C^*$-subalgebras of a given $C^*$-algebra.
UR - http://bims.iranjournals.ir/article_357.html
L1 - http://bims.iranjournals.ir/article_357_bceaa5c7dfeb6e2303668f1f6eee51b4.pdf
ER -